The reliability of machine learning (ML) software systems is heavily influenced by changes in data over time. For that reason, ML systems require regular maintenance, typically based on model retraining. However, retraining requires significant computational demand, which makes it energy-intensive and raises concerns about its environmental impact. To understand which retraining techniques should be considered when designing sustainable ML applications, in this work, we study the energy consumption of common retraining techniques. Since the accuracy of ML systems is also essential, we compare retraining techniques in terms of both energy efficiency and accuracy. We showcase that retraining with only the most recent data compared to all available data reduces energy consumption by up to 25%, being a sustainable alternative to the status quo. Furthermore, our findings show that retraining a model only when there is evidence that updates are necessary, rather than on a fixed schedule, can reduce energy consumption by up to 40%, provided a reliable data change detector is in place. Our findings pave the way for better recommendations for ML practitioners, guiding them toward more energy-efficient retraining techniques when designing sustainable ML software systems.